Implicit neural representation takes a neural network as the continuous mapping function between the spatial coordinates and the scene properties. Shape-conditioned representations concatenate the coordinate \(\mathbf {x} \)  and a latent shape embedding \(\mathbf {z}\)  to represent multiple shape instances as \(\mathbf {y}=f(\mathbf {x}, \mathbf {z};\theta )\) . The shape embedding \(\mathbf {z}\)  is latter conducted in a local fashion to recover fine-grained details at scene scale [1]}, [2]}, [3]}. The output properties \(\mathbf {y}\)  infered from the shape-conditioned representations vary across shape [4]}, [5]}, [6]}, appearance [7]}, [8]}, [9]}, and motion [10]}. Another line uses neural networks to regress the parameters of decomposed primitives directly from the input point set as \(\lbrace \mathbf {m}_j\rbrace  = f(\lbrace \mathbf {x}_i\rbrace ; \theta )\) . The regressed primitive parameters are then grouped together as the entire shape parameter space, representing the scene geometry as \(\mathbf {y} = \phi (\lbrace \mathbf {m}_j\rbrace , \mathbf {x})\) . Commonly used primitives include hyperplanes [11]}, Gaussian mixtures [12]}, [13]}, [14]}, volumes [15]}, and local planes [16]}.
